Sobolev and Hardy-Sobolev spaces on graphs

Emmanuel Russ (1) , Maamoun Turkawi (2)

1 IF - Institut Fourier
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

Let $\Gamma$ be a graph. Under suitable geometric assumptions on $\Gamma$, we give several equivalent characterizations of Sobolev and Hardy-Sobolev spaces on $\Gamma$, in terms of maximal functionals, Haj\l asz type functionals or atomic decompositions. As an application, we study the boundedness of Riesz transforms on Hardy spaces on $\Gamma$. This gives the discrete counterpart of the corresponding results on Riemannian manifolds.

Mots clés: Hardy spaces; Sobolev spaces; maximal characterizations; Poincaré inequalities; graphs; Riesz transforms

Domaines: Analyse classique [math.CA]

Emmanuel Russ, Maamoun Turkawi. Sobolev and Hardy-Sobolev spaces on graphs. 2012. ⟨hal-00740820⟩